Abstract
The lattice vibrational properties of $\ensuremath{\alpha}\text{\ensuremath{-}}\mathrm{Sn}$ (gray tin) were investigated experimentally by temperature-dependent x-ray diffraction and theoretically by density functional theory calculations. Similar to the other elements of group IV, $\ensuremath{\alpha}\text{\ensuremath{-}}\mathrm{Sn}$ exhibits a lattice anomaly at low temperatures and negative thermal expansion, with a minimum at $\ensuremath{\sim}27\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ and a magnitude three times larger than in Si. The influence of anharmonic effects up to fourth-order potential terms on the phonon dispersion relations, the lattice parameters, and the thermal expansion coefficient have been tested. The performed analysis gives an excellent agreement with experiment when quartic potential terms are included in the theory. We point out that negative thermal expansion in $\ensuremath{\alpha}\text{\ensuremath{-}}\mathrm{Sn}$ is not driven by the anharmonicity of the interatomic potential. This resolves the long-standing puzzle in the thermal behavior of $\ensuremath{\alpha}\text{\ensuremath{-}}\mathrm{Sn}$.
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